Potentials wells in high dimensions II, more about the one well case
Propagating edge states for a magnetic Hamiltonian.
Propagation estimates for N-body Stark hamiltonians
Propriétés de la matrice de diffusion, 2-amas 2-amas, pour les problèmes à N corps à longue portée
Pseudo-bosons from Landau levels.
Quantization on submanifolds
Recent Results on the Cauchy Problem for Focusing and Defocusing Gross-Pitaevskii Hierarchies
In this paper, we review some of our recent results in the study of the dynamics of interacting Bose gases in the Gross-Pitaevskii (GP) limit. Our investigations focus on the well-posedness of the associated Cauchy problem for the infinite particle system described by the GP hierarchy.
Relativistic stability of matter (I).
In this article, we study the quantum mechanics of N electrons and M nuclei interacting by Coulomb forces. Motivated by an important idea of Chandrasekhar and following Herbst [H], we modify the usual kinetic energy -∆ to take into account an effect from special relativity. As a result, the system can implode for unfavorable values of the nuclear charge Z and the fine structure constant α. This is analogous to the gravitational collapse of a heavy star. Our goal here is to find those values of α...
Resonance theory for periodic Schrödinger operators
Semiclassical asymptotics for exchange energy
Semiclassics of the quantum current in very strong magnetic fields
We prove a formula for the current in an electron gas in a semiclassical limit corresponding to strong, constant, magnetic fields. Little regularity is assumed for the scalar potential . In particular, the result can be applied to the mean field from magnetic Thomas-Fermi theory . The proof is based on an estimate on the density of states in the second Landau band.
Solitons and Gibbs Measures for Nonlinear Schrödinger Equations
We review some recent results concerning Gibbs measures for nonlinear Schrödinger equations (NLS), with implications for the theory of the NLS, including stability and typicality of solitary wave structures. In particular, we discuss the Gibbs measures of the discrete NLS in three dimensions, where there is a striking phase transition to soliton-like behavior.
Stability of matter in classical and quantized fields.
Stark resonances for random potentials of Anderson type
SUSY quantum Hall effect on non-anti-commutative geometry.
Système à corps dans un champ magnétique
The Cauchy problem for Hartree-Fock time-dependent equations
The inverse -body problem. A geometrical approach
Topological quasi *-algebras and the time evolution of systems
We give here a survey of some recent results on applications of topological quasi *-algebras to the analysis of the time evolution of quantum systems with infinitely many degrees of freedom.
Transport in thermal equilibrium, gapless modes, and anomalies